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Radoslav Tsvetkov edited comment on MATH878 at 10/15/12 8:14 AM:

Hi Ted,
Signed Root LLR is a really good idea! I added the test (also in TestUtilsTest)
And some comment on signed rLLR:
In some cases of unexpectedly small similar p1 and p2 values
or large anomalies of k11, ... counts it is desired to
get additional information on the rate trough signed root LLR.
Signed root LLR has two advantages over the basic LLR:
a) it is positive where k11 is bigger than expected, negative where it is
lower. This resolves your current problem.
b) if there is no difference it is asymptotically normally distributed.
This allows people to talk about "number of standard deviations" which is a
more common frame of reference than the chi^2 distribution.
See Discussions at: ....
was (Author: rtsvet):
Hi Ted,
Signed Root LLR is a really good idea! I added the test (also in TestUtilsTest)
And some comment on signed rLLR:
In some cases of unexpectedly small similar p1 and p2 values
* or large anomalies of k11, ... counts it is desired to
* get additional information on the rate trough signed root LLR.
*
* Signed root LLR has two advantages over the basic LLR:
* a) it is positive where k11 is bigger than expected, negative where it is
* lower. This resolves your current problem.
* b) if there is no difference it is asymptotically normally distributed.
* This allows people to talk about "number of standard deviations" which is a
* more common frame of reference than the chi^2 distribution.
*
* See Discussions at: ....
> GTest (LogLikelihood ratio  LLR test) in math.stat.inference
> 
>
> Key: MATH878
> URL: https://issues.apache.org/jira/browse/MATH878
> Project: Commons Math
> Issue Type: New Feature
> Affects Versions: 3.1, 3.2, 4.0
> Environment: Netbeans
> Reporter: Radoslav Tsvetkov
> Labels: features, test
> Fix For: 3.1
>
> Attachments: MATH878_gTest_12102012.patch, MATH878_gTest_15102012.patch, vcsdiff16294.patch
>
> Original Estimate: 24h
> Remaining Estimate: 24h
>
> 1. Implementation of GTest (LogLikelihood ratio LLR test for independence and goodnesoffit)
> 2. Reference: http://en.wikipedia.org/wiki/Gtest
> 3. ReasonsUsefulness: Gtests are tests are increasingly being used in situations where
chisquared tests were previously recommended.
> The approximation to the theoretical chisquared distribution for the Gtest is better
than for the Pearson chisquared tests. In cases where Observed >2*Expected for some cell
case, the Gtest is always better than the chisquared test.
> For testing goodnessoffit the Gtest is infinitely more efficient than the chi squared
test in the sense of Bahadur, but the two tests are equally efficient in the sense of Pitman
or in the sense of Hodge and Lehman.

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